Wednesday, August 30, 2006

Most people in developed countries can easily use their assets to secure credit. With a stable source of income or a bit of collateral, like a house or a car, an American can take out a loan to start a business, remodel the bathroom, or buy an engagement ring.

Poor peoples' incomes are inherently less stable and often too low to qualify for lending. The ill-defined property rights in many developing nations make it difficult for poor residents to prove that they own the housing or land that they occupy. Lacking both income and legitimate titles to what little collateral they actually have, the credit prospects for most of the world's poor seem bleak.

Enter microcreditors. As Tyler Cowen describes in his latest Economics Scene column for The New York Times, microcreditors are non-profit, for-profit, or government organizations that lend small sums to people in poor communities. The microloan recipients open businesses, improve their homes, or pay medical bills--using the loans to invest or consume as they see fit. Read Cowen's commentary to find out more about the benefits and controversies surrounding microcredit in India.

1. According to Cowen, microlenders like Spandana offer poor Indians better rates than traditional money lenders. How do the lending practices of microcredit organizations differ from the practices of traditional money lenders? How does Spandana use community pressure to maintain high repayment rates among its loan recipients? What other incentives encourage borrowers to repay the microloans?

2. Why do some state officials in India oppose the practices of microcreditors like Spandana? According to Cowen, what would legal caps on interest rates do to the solvency of microcreditors? How might legal caps on interest rates change the borrowing habits of India's poor?

3. Cowen visited Hyderabad--a metropolis of over 6 million residents. He suggests that microlending works fairly well for poor people in this urban setting. How might the feasibility of microcredit change in a rural setting? Rural residents in developing countries earn income from farming--a relatively risky vocation because of price volatility and unpredictable weather. Would repayment rates among rural residents likely be higher or lower than those among urban residents? How would traveling to rural settings affect the way microcreditors monitor repayment?

Monday, August 28, 2006

The New York Times reports that real wages, as a percentage of GDP, have fallen to their lowest level in recorded history. The article contains a number of good nuggets that illustrate some basic points in economics.

First, we need to think about what we mean by "wages." A worker's nominal wages are the dollar value of her take-home pay, not including benefits. For example, if a worker earns $20 per hour before taxes, that is her nominal hourly wage. However, a worker's real wages are the wages adjusted for inflation. For example, if a worker's nominal wage rises by 2% and there is 3% inflation, we actually consider her real wages to have dropped by 1%--that is, the value of goods and services she could afford went down by 1%. (In fact, real wages did decrease in 2005: median weekly earnings increased from $631 to $651, an increase of 3.16%, but since inflation was at 3.4%, the $651 in 2005 was actually worth less than the $631 in 2004.)

However, the article doesn't say that real wages have decreased--indeed, with the exception of 2005, real wages have generally increased over the last few years. The article's main point is that as a percentage of GDP, real wages have been steadily declining. In other words, the growth rate of GDP has been steadily greater than the growth rate of wages and salaries.

But that's only part of the story, because wages are just part of workers' overall compensation packages. Health insurance is the other big component. Due to a historical anomaly, employers tend to pay for health insurance for their workers, rather than workers buying it on their own. Therefore, total compensation to workers can be thought of has having two components: wages, which the workers are free to spend as they wish, and a certain amount of money with which they are forced to buy health insurance. In recent years, the price of health insurance has grown at double-digit rates, far outpacing inflation, while wages, as a fraction of the overall compensation package, have been falling.

Note that the increase in health care spending might very well have had the same effect if workers received all of their compensation in cash, and then paid for health insurance out of their own pockets. Since health care is widely viewed as a necessity rather than a luxury, demand for it is relatively inelastic; therefore, as its price goes up, people might very well decrease their expenditures on other goods and services. In other words, the effect of an increase in the price of healthcare means a decrease in consumers' real income, and the fact that wages and salaries don't include benefits serves to highlight this effect.

However, even if we take into account both wages and benefits, overall compensation has still been falling in recent years as a fraction of GDP, while corporate profits have been increasing. Why? Workers have been more productive--that is, creating more output per hour of labor--which has meant higher revenues for firms. Those revenues accrue to different factors of production: wages to workers, rent to capital, and profits to shareholders. The article's main point is that the gains in worker productivity have not accrued to workers, but instead have gone largely to shareholders.

Describing how wages, benefits, and profits have changed over past years is the province of positive analysis. The article raises an important normative question as well: is it fair that wages have not kept pace with productivity? Or that the top 1% of earners received over 11% of all wage income, up from 6% three decades ago? These are important questions as well, but economic analysis is less helpful in answering them.

1. Suppose the U.S. government provided national health insurance for everyone. Do you think wages and salaries would still be falling? What about after-tax wages?

2. The divvying up of the economic pie appears to be a zero-sum game: there is a certain amount of economic surplus out there to be divided between profits and wages, and more of it has been going to profits. Jared Bernstein, a senior economist at the Economic Policy Institute, lays the blame for lower real wages on workers' lack of bargaining power. Would a greater rate of unionization help to achieve greater equity? Would it do so at the expense of efficiency? What about using government taxes and transfers to achieve greater redistribution of income from rich to poor households? Would economic policies aimed at a more equitable division of the economic pie mean a decrease in the size of the pie?

3. If labor markets were perfectly competitive, wages would increase directly with productivity. (For a simulation of how this works, see this demonstration of an interactive experiment based on the classical theory of the labor market.) What about the real labor market is a departure from this model?

Update: This has been a hot topic on the blogosphere. Greg Mankiw, Russell Roberts, and David Altig have posted comments on the article (and others' comments on it). More to follow, I'm sure, and we'll keep you updated.

Monday, August 21, 2006

Argentina is no stranger to inflation and has suffered frequent periods of devastating inflation since 1945. Despite recent praise from the International Monetary Fund for its economic growth, Argentina currently suffers from a 12.3% inflation rate (compared to only 4% in the United States).

Milton Friedman, winner of the 1976 Nobel Prize in Economics, compares inflation to alcoholism in his PBS series, Free to Choose:

Inflation is just like alcoholism, in both cases, when you start drinking or when you start printing too much money. The good effects come first; the bad effects only come later. That's why, in both cases, there is a strong temptation to overdo it, to drink too much and to print too much money. When it comes to the cure, it's the other way around, when you stop drinking or when you stop printing money the bad effects come first and the good effects only come later. That's why it's so hard to persist with the cure.

Source: Free to Choose, Volume 9 of 10, How to Cure Inflation (26:40)

A simple aggregate demand (AD) and aggregate supply (AS) diagram offers great insight into Friedman's analogy and Argentina's inflation woes. The following AD-AS diagram is based on a paper by Professor David Romer. The model might be slightly different from the AD-AS diagram in your textbook.

First, let's look at the assumptions in the model. The aggregate demand curve (AD) assumes that the central bank raises the interest rate in order to combat inflation. For example, if the inflation rate increases, then the central bank will raise the interest rate to reduce consumption and investment, thereby lowering output. The short-run aggregate supply curve (SRAS) represents the inflation rate. The long-run aggregate supply curve represents the output level where the inflation rate has no tendency to change. The long-run aggregate supply curve is often referred to as potential output or full-employment output.

Second, let's look at the short-run effects of an increase in the money supply. In the short run, economists assume that the inflation rate is temporarily fixed. The short run might be a period of 1 day, 1 month, or 1 year. There is no consensus about how long the short run lasts. If the central bank expands the money supply, then the interest rate falls. A fall in the interest rate stimulates consumption and investment spending which shifts the aggregate demand curve to the right from AD1 to AD2.The good effects come first--in the short run, it seems as though the economy has benefited from a higher quantity of money. Output increased from $450 billion to $500 billion which creates more jobs without increasing inflation.

Third, let's look at the long-run effects of an increase in the money supply. The output level at time B is not a sustainable amount of output because $500 billion exceeds full-employment output, which is only $450 billion. An output level above the full-employment output necessarily means that resources in the economy are being over-utilized. Inflation expectations increase in the long run as a consequence of over-utilization, which causes the inflation rate to gradually increase from SRAS1 to SRAS2.

As the inflation rate increases, the central bank frantically tries to contain inflation by increasing the interest rate which reduces output gradually from $500 billion to $450 billion.The bad effects come later--in the long run, the monetary expansion leads to soaring inflation without creating any new jobs. Historically, a high inflation rate is associated with lower rates of long-run economic growth. High inflation rates create uncertainty about future production costs and the future purchasing power of the currency. As a result, high inflation tends to discourage saving and investment--both important determinants of long-run economic growth.

The following graphs show the time path for the inflation rate and output between time A and time E. Notice that the good effects occur between time A and B, but the bad effects occur between times B and E.1. Despite the central bank's attempts to reduce inflation between times B and E, the inflation rate inevitably still increases. What can explain this?

2. Suppose the economy is at time E. What must Argentina's central bank do in order to reduce the inflation rate from 12% to 2%? Will this be politically popular?

3. Using the AD-AS model, explain what Friedman means by "When it comes to the cure, it's the other way around, when you stop drinking or when you stop printing money the bad effects come first and the good effects only come later. That's why it's so hard to persist with the cure."

Friday, August 18, 2006

The EDS Corporation's cat herding commercial is good for a laugh, but Barun Mitra--director of the Liberty Institute--is entirely serious about tiger ranching in China and India. According to Mitra, tiger pelts sell for as much as $20,000 on the black market and growing demand for traditional Chinese medicines makes other parts of the tiger lucrative as well. The currently illegal trade in tigers and tiger parts presents an increasingly valuable opportunity for poachers. Poaching, in turn, plays a significant role in keeping the tiger close to extinction. Mitra believes a legal market for tiger parts will save the tiger from extinction. Read his op-ed column in The New York Times to see why.

1. What is the current approach to tiger conservation in India and China?

2. Mitra points out that farmers and ranchers have a strong incentive to ensure that marketable species of livestock (sheep, cattle, chickens, and the like) do not go extinct. Does his argument for conservation through market mechanisms apply to other wild endangered species? Do tigers need to be ranched like cattle in order to give humans an incentive to conserve them?

3. Consider an alternative to outright tiger ranching. Mitra cites a program in Zimbabwe where villagers had property rights on local wildlife. How did the villagers use their property rights to earn money? What conservation incentives did they face? Would similar programs in China and India reduce the threat of tiger extinction? How would villagers with property rights on tigers feel about poachers?

4. Is poaching the only thing keeping tigers close to extinction? What about habitat encroachment? Could a legal market in tiger parts or licensed tiger hunting help to preserve tiger habitat?

Wednesday, August 16, 2006

Early in the recent conflict between Israel and Lebanon, Kai Ryssdal, the anchor on the public radio program"Marketplace," conducted two interviews: one with an Israeli civilian living in Haifa and another with a journalist living in Beirut. He didn't ask for their feelings and opinions about the war. Instead, he talked to them about the details of their everyday economic lives.

The parallels were striking. Each talked primarily about the supermarkets, or more particularly, what wasn't in the supermarkets. In Israel, there was no bread or milk, because the delivery drivers didn't want to risk being on the roads; in Lebanon, there were long lines for the little that remained. (Remember, too, that these interviews were early in the conflict--as the weeks went on, what little had stocked the shelves was long gone.)

Both interviewees talked about the dangers of travel on the roads. The Israeli military viewed Lebanese roads as strategic targets, and being on the open road in Israel left one vulnerable to rocket attacks.

When we learn about comparative advantage in economics, the theory is rosy. The market, after all, coordinates the efforts of complete strangers from many different countries to produce a product as seemingly simple as a pencil. Missing from most of these discussions are the assumptions underlying the free flow of international trade, including, most importantly, the assurance that the cargo and its transporter will arrive safely at their destination.

In other words, gains from trade can only be realized when the infrastructure is there to support it. It only takes a few days of shelling in the Middle East--or a few days without clean water and electricity in New Orleans--to remind us that the economic web we depend on can be quite fragile.

1. One of the arguments against free trade is that it is unreasonable to depend on foreign suppliers of essential goods like food and energy. Yet free trade also yields incredible benefits. How does an economist balance these two arguments? How would you go about finding the optimal level of domestic and foreign production? Why might the optimal choice for Israel be different than the optimal choice for, say, Singapore or the United States?

2. Economies of scale exist when a few large firms can produce a good or service at a much lower cost than many small firms. For example, massive farms have become the norm in the United States, where a century ago small farms dominated (but had much higher costs). How much of the food you eat comes from farms within 10 or 20 miles of your home? In the case of a major emergency, how long would it take for food shortages to become a major problem? Would the United States be better off if everyone still owned a farm--or are the gains from trade we've realized from specialization large enough to offset that change? How can you tell?

3. The interviewees talk about how expensive it is for Lebanese to evacuate Beirut, and how difficult it is to get cash from ATMs in Israel. Think about the implications of sustained political upheaval on economic growth. In some ways, war acts like a tax, making everything more expensive. Try drawing some supply and demand diagrams for various goods, and guess as to what happens to those markets in times of turmoil. What could the governments of Israel and Lebanon do, if anything, to help alleviate the economic suffering of their people?

Monday, August 14, 2006

Newspaper ads on every college campus beckon cash-strapped students to sell their plasma, sperm, or eggs to the appropriate medical intermediaries. It's Adam Smith's invisible hand at work: People need plasma for blood transfusions; students with excess plasma need cash. Plasma banks facilitate the transaction and everyone's better off.

The enterprising student will wonder whether he can collect on other spare parts--say, a kidney. He cannot. The sale of human organs, whether it benefits a living kidney donor or the family members of a recently deceased heart donor, is illegal in the United States. Why, asks the latest Freakonomics column, is selling a kidney illegal in a country where thousands of people die each year waiting for kidney transplants? Read the column to see what Stephen Dubner and Steven Levitt have to say about the organ shortage.

1. Suppose the graph above represents a market for transplantable kidneys from live donors. Under current law, the price of a kidney is restricted to zero. At a zero price, 15,000 people (most likely friends and family of the recipients) supply a kidney to eligible patients each year. What's the shortage of kidneys at a zero price?

2. Beyond the 15,000 charitable donors our hypothetical supply curve takes a more familiar, upward-sloping shape. Each point on the supply curve represents the seller's cost of providing a transplantable kidney. According to Dubner and Levitt, what are some of the costs that influence the supply decisions of living kidney donors? (Think about forgone wages, medical risks, and the fact that supplying a kidney is a one-time event.)

3. In our hypothetical market for kidneys shown in the graph, what price clears the transplantable kidney market? (See an actual economic estimate of kidney prices in this paper by Gary Becker and Julio Jorge Elias.) Notice that closing the kidney shortage with a free market adds to the cost of a transplant (already upwards of $200,000). Might the additional cost of procuring a kidney price some patients out of the market altogether? That is, would an increase in the price of a transplant reduce the quantity of transplants demanded? Do you think the quantity of transplants demanded is sensitive or insensitive to price (is the price elasticity of demand for transplants perfectly inelastic)?

4. If you're like most normal people, the prospect of a market for kidneys raises all kinds of moral and ethical questions. According to the column, Alvin Roth helped devise a program that uses incentives to elicit organ donations from strangers, but stops short of a free market for organs. How does the New England Program for Kidney Exchange align the incentives of non-related donors and recipients without monetary incentives?

5. Kidneys from living donors are preferable from a medical perspective, but usable organs from the recently deceased are important as well. Of course, doctors can't just go around harvesting organs every time someone dies. Americans, usually at the Department of Motor Vehicles, have to sign-up if they wish to donate usable organs upon death. What would happen to the organ shortage in the United States if all Americans were donors by default?

Check out the Freakonomics website for more about creative solutions to the organ shortage.

Thursday, August 10, 2006

Microeconomists examine how the BP oil field shutdown affects oil prices, the behavior of automobile drivers, and profitability of particular industries. Oil Shock, Part I showed that the oil field shutdown raises the price of oil which reduces the profitability of many firms.

Macroeconomists, on the other hand, examine the economy-wide effects such as how a sharp rise in oil prices affects inflation, output, and unemployment. Suppose that the BP oil field shutdown causes the inflation rate to increase from Inflation Rate 1 to Inflation Rate 2 because firms try to pass on some of the higher input prices to higher output prices. In order to simplify the analysis, assume that full-employment output is constant at FE Output. Full-employment output, or potential output, is the amount of output that the economy produces when all the resources in the economy are efficiently utilized.

If the BP oil field shutdown increases the inflation rate, then the Fed will pursue a tight (anti-inflation) monetary policy which raises interest rates. Higher interest rates would reduce consumption and investment, causing output to fall. An output gap opens up as actual output falls below full-employment output in the short run. In the long run, the output gap will cause the inflation rate to fall back to its initial state. As the inflation rate falls in the long run, the Fed will pursue loose monetary policy and return the economy back to full employment.

A fall in output usually leads to an increase in the unemployment rate as firms cut back on production of goods and services and lay-off workers.

If the BP oil field shutdown leads to an inflation shock, then interest rates will rise, output will fall, and unemployment will increase in the short run.

However, inflation's tyranny does not end there. A higher inflation rate also destroys wealth in terms of stocks and bonds. An increase in the interest rate also reduces the price of stocks and bonds (archived entry: Why Does Bernanke's Small Talk Move Markets?)

1. Financial markets are very sensitive to inflation data. Suppose the Bureau of Labor Statistics reports that the inflation rate increased from 2% to 4%. Why would stock and bond prices fall as soon as the report is released, but before the Fed actually changes any interest rates?

2. The Fed, in its last FOMC meeting on August 8, 2006, kept the federal funds rate unchanged at 5.25%. Could this mean that the Fed does not consider the BP oil field shutdown an inflation shock?

3. Inflation expectations matter. The Fed's inflation-fighting credibility has been strong since Paul Volcker (the Federal Reserve Chairman from 1979 to 1987). Suppose consumers and producers always expect the Fed to return the economy to a target inflation rate--would higher oil prices require the Fed to raise interest rates (or raise them by as much)?

Economists use the term "supply shock" to refer to an unexpected event that causes a sharp change in the supply of a good. A classic example occurred recently when BP closed down the Prudhoe Bay oil field after finding "unexpectedly severe corrosion" in a pipeline. Pumping about 400,000 barrels per day, the pipelines from Prudhoe Bay carry about 8% of the nation's domestic oil production.

The chain of events that followed the announcement of the shutdown present a textbook example of economics in action. According to the New York Times:

Word of the shutdown rattled global commodities and equities markets. In the United States, oil prices rose more than two dollars a barrel. The benchmark contract for light, sweet crude to be delivered next month rose as high as $77.30 a barrel before settling at $76.98 a barrel in New York trading. Prices rose even higher in London, where Brent crude for September delivery closed at a record $78.30 a barrel…

Stocks, meanwhile, fell in American trading and slid across Europe. Major indexes in Britain, Germany and France all posted substantial declines for the day.

In microeconomic terms, the Prudhoe Bay closure shifts the supply curve of oil to the left, increasing the equilibrium price and decreasing the quantity of oil in the market (Figure A). Because oil is so important for the production of goods and services, an increase in its price will increase business costs worldwide (Figure B). Because higher costs reduce firms' profits, investors bid down stocks in equity markets.

See Part II of this post for the macroeconomic impact of this supply shock.

1. Why do unexpected changes, such as this one, impact the stock market so much more than expected changes?

2. Which goods and services are most affected by changes in the price of oil? Draw a supply and demand diagram for one of those goods. How will the closing of the oil field affect the market you chose?

3. BP has been plagued by safety problems in the past few years. Like any company, it faces a tradeoff between safety and profitability. Using cost-benefit analysis, how would you find the optimal level of safety? Do you think BP chose the optimal level, or do you think it spent too little on safety? How could you find out the answer to that question?

Thursday, August 03, 2006

During the 1960s and early 70s, economists--including Milton Friedman of the University of Chicago--made a strong case for ending the draft, the government practice of forcing people to join the military. Those who supported the draft at the time argued that an all-volunteer military would be far too expensive. Eliminating conscription would force the military to pay higher wages in order to attract young men. Higher pay would cripple the military, especially during Vietnam.

The response from Friedman and other draft opponents? Sure, the draft lowers the budgetary cost of building up a military, but only at a massive opportunity cost. Those who join the military because of the draft or the fear of being drafted do so against their will. Most draftees (if not entirely opposed to military service) would require a higher level of pay in order to enlist as a true volunteer. Conscription forces people into service at lower pay than they would otherwise earn. That is, draftees pay a conscription "tax" in order to finance the nation's military build-up. The conscription tax is equal to the difference between the pay draftees would earn in the absence of the draft and the military pay they earn because of it. Better, according to Friedman, to abolish the draft altogether and have all tax payers bear the costs of maintaining an army of soldiers who voluntarily accept their posts and pay.

Draft opponents won the day Congress allowed the law authorizing the draft to expire on June, 30 1973. Why, then, is Charles Wheelan--another University of Chicago economist--calling for a return to conscription? Read his latest Yahoo! Finance column to find out.

As Wheelan points out, moral hazard occurs when people behave differently--and sometimes recklessly--because they don't bear the full costs of their actions. Mountain climbers may take riskier routes because they know there's a good chance search and rescue can find them if they get stranded. Insured drivers may exercise less caution because their policy reduces the cost of getting in an accident. Auto insurers address moral hazard by requiring deductibles--a sum that the driver must pay on a claim before the insurance kicks in. If drivers understand that they'll pay the first $1,000 for any damages from an accident, they may drive a bit more cautiously.

Wheelan applies this theory to U.S. foreign policy, arguing that an unintended consequence of the all-volunteer army is that it makes the electorate more likely to support U.S. military involvement in overseas conflicts.

1. Wheelan proposes a modified draft. In what ways is his proposal like the deductible on your auto insurance policy? Do we need another conscription tax to put a check on our troop commitments in times of humanitarian crisis?

2. How is deficit financing (issuing government bonds instead of collecting taxes) like the moral hazard problem surrounding foreign intervention and invasion by the U.S. military?

3. In what way is Wheelan's proposal subject to the same criticism Friedman leveled against the draft nearly 40 years ago?

4. Despite enlistment bonuses and aggressive recruiting, the U.S. military has had difficulty increasing manpower during the Iraq war. Politicians and the electorate cannot decide to invade or intervene if would-be soldiers won't enlist. Do you think the free market for military labor that Friedman championed provides enough of a check on the moral hazard of a volunteer army? Or do you agree with Wheelan that some form of conscription is needed to discourage hazardous decision making?

To read more about the role economists played in ending the draft, click here.

Tuesday, August 01, 2006

Suppose you have two things in your wallet: a $20 bill and a frequent flier card. Which of these is considered money?

The formal definition of money is that it is (1) a medium of exchange, (2) a store of value, and (3) a unit of measure. The $20 bill clearly meets all three. The frequent flier miles are a tougher question.

These days, you can use frequent flier miles for a lot more than just booking plane tickets. Airlines have cross-promotions with magazines and home entertainment stores that enable you to cash in your miles for all kinds of goodies. At the same time, it's getting tougher to actually fly with frequent flier miles, as airlines reduce the number of seats eligible for frequent flier redemptions. Even if airlines stopped issuing miles, it would take people years to draw down their current stash of frequent flier miles. Hence, the pressure to create uses for miles that don't involve air travel, making miles a true medium of exchange.

In many ways, then, frequent flier miles act as a sort of mirror currency. Are they a good store of value, though? With airline bankruptcies mounting, David A. Kelly of the New York Times offers some free "Advice to Mileage Misers: Use the Hoard Now." He argues that evaporating opportunities to use miles amount to inflation of the frequent flier currency. That is, as the airlines reduce the number of redeemable seats, the purchasing power of frequent flier miles falls. Kelly quotes Tim Jarrell, publisher of Fodor's Travel Publications: "They're not bank accounts that earn interest." Another interesting quote from the article:

"Frequent-flier programs have turned into trading stamp programs without the stamps," said Terry Trippler, spokesman for CheapSeats.com. "Instead of opening up more seats for travelers, most programs are now offering magazine subscriptions, gift certificates or merchandise such as TVs instead. I sometimes wonder if the TV sets they're offering will last longer than the airlines themselves."

1. There are lots of other things that act like currency in our society, from Starbucks stored value cards to credits on iTunes. Some are even purely virtual, like currency in online fantasy games like Ultima. (See this BBC News article. Interestingly, the Gaming Open Market that it refers to is now closed, with a rather humorous sign-off.) Can you name a few more? What do they have in common with cash? What differentiates them from traditional currency? Do any of the stored value cards or credit systems gain value over time; are any of them worth hoarding?

2. A $20 Starbucks stored value card is clearly worth less than a $20 bill. Why do people buy stored value cards at face value?

3. Kelly has many useful nuggets of advice for using up your frequent flier miles. In many cases, he says, a trip from point A to point B may be possible, but it's made difficult because there are many possible routes that need to be checked. For example, he cites a case in which agents tell customers it's impossible to fly to Asia on frequent flier miles, while it is in fact possible, but only if you go through Amsterdam, which takes a bit longer. Why is it profitable for airlines to make it difficult to redeem miles? Is there an optimal level of difficulty? If you were in charge of an airline frequent-flier program, how would you find that optimal level?